Having read "The Strange Encounter of Kenta 4", I wonder why the reading 「えがく」 for 「描く」 is used. I thought the correct reading would be 「かく」in this case? It would be nice if somebody could clarify if both readings are correct and in what case to use one ore the other reading.

Both えがく and かく are correct (another kanji for this verb is 画く i think).

Merci bien - thank you for your reply. The reason I came up with this topic is because my teacher (a native speaker) corrected me when I was using the reading「えがく」instead of 「かく」 in a sentence containing 「絵を描く」. I looked up the corresponding section in "The Strange Encounter of Kenta 4" afterwards and found that the reading「えがく」was used there. Unfortunately I did not have the chance to discuss this with my teacher again. So I did a search via Google and I found the following thread: http://oshiete.goo.ne.jp/qa/5959818.html.
My Japanese is not good enough to understand the whole discussion, but it seems that「かく」is most commonly used in this case. One of the reason for this seems to be that when reading「絵を描く」as 「えをえがく」this would be some kind of redundancy that sounds a bit strange?
My current understanding is, that「えをえがく」is not so usual as a reading and I wonder why it is used in "The Strange Encounter of Kenta 4". This would be interesting to know. Or am I completely wrong about this and both are used in everyday Japenese to the same extend?

描く can be pronounced えがく or かく. The latter pronunciation was officially added to the Jouyou in 2010 whereas the former was already part of the Jouyou.

In every day life, it's very common to hear Japanese say えをかく. Someone in the forum you were referring to feels えがく is a little more polite, and my Japanese wife also feels this way. In the text the old lady is about 80 years old, and we wanted to give her a smart, gentle and quiet personality, and in this sense make her words more polite.

I'll add a comment to make things clearer in the text or change it to かく so that people don't get confused.

Thank you very much Raphael - your reply was exactly the kind of response I was hoping for. Now I understand why you used this particular reading in this situation.

As it's perhaps only me who got a bit confused about this, adding a comment to the text would probably be the best (and easier) solution. I think with the information (for beginners like me) that both readings are correct and a short explanation, why you are using this reading in this situation, everybody will have enough information to understand. For me (at my level of knowledge), it's very helpful to get this kind of explanation (why do you use something in a particular case) to build up a feeling for the language.

And last but not least something off-topic: A very, very big "thank you!" for the reading assistant! The stories I read so far are entertaining, the range of the difficulty level is perfect and especially the Android App with the possibility to display furigana and JLPT level kanji highlighting are great. This is a really helpful tool to study Japanese. (Second thought: I have to post the last remark on Google Play to promote the app...)